scholarly journals The Walsh Transform of a Class of Boolean Functions

2021 ◽  
Vol 26 (6) ◽  
pp. 453-458
Author(s):  
Niu JIANG ◽  
Zepeng ZHUO ◽  
Guolong CHEN ◽  
Liting WANG
Keyword(s):  
Boolean Functions ◽  
Walsh Transform ◽  
Trace Function ◽  
Existing Result

The Walsh transform is an important tool to investigate cryptographic properties of Boolean functions. This paper is devoted to study the Walsh transform of a class of Boolean functions defined as [see formula in PDF], by making use of the known conclusions of Walsh transform and the properties of trace function, and the conclusion is obtained by generalizing an existing result.

Characterizing Linear Structures of Boolean Functions from Arithmetic Walsh Transform

2017 ◽  
Vol E100.A (9) ◽  
pp. 1965-1972
Author(s):  
Qinglan ZHAO ◽  
Dong ZHENG ◽  
Xiangxue LI ◽  
Yinghui ZHANG ◽  
Xiaoli DONG
Keyword(s):  
Boolean Functions ◽  
Walsh Transform ◽  
Linear Structures

scholarly journals Several new classes of (balanced) Boolean functions with few Walsh transform values

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Tingting Pang ◽  
◽  
Nian Li ◽  
Li Zhang ◽  
Xiangyong Zeng ◽  
...  
Keyword(s):  
Boolean Functions ◽  
Walsh Transform

scholarly journals Improving bounds on probabilistic affine tests to estimate the nonlinearity of Boolean functions

2021 ◽  
Author(s):  
Ana Sălăgean ◽  
Pantelimon Stănică
Keyword(s):  
Lower Bound ◽  
Boolean Functions ◽  
Good Accuracy ◽  
Arbitrary Order ◽  
Probability Of Failure ◽  
Probabilistic Methods ◽  
Walsh Transform ◽  
The One ◽  
Almost All ◽  
Linearity Test

AbstractIn this paper we want to estimate the nonlinearity of Boolean functions, by probabilistic methods, when it is computationally very expensive, or perhaps not feasible to compute the full Walsh transform (which is the case for almost all functions in a larger number of variables, say more than 30). Firstly, we significantly improve upon the bounds of Zhang and Zheng (1999) on the probabilities of failure of affinity tests based on nonhomomorphicity, in particular, we prove a new lower bound that we have previously conjectured. This new lower bound generalizes the one of Bellare et al. (IEEE Trans. Inf. Theory 42(6), 1781–1795 1996) to nonhomomorphicity tests of arbitrary order. Secondly, we prove bounds on the probability of failure of a proposed affinity test that uses the BLR linearity test. All these bounds are expressed in terms of the function’s nonlinearity, and we exploit that to provide probabilistic methods for estimating the nonlinearity based upon these affinity tests. We analyze our estimates and conclude that they have reasonably good accuracy, particularly so when the nonlinearity is low.

scholarly journals Parallel Fast Walsh Transform Algorithm and Its Implementation with CUDA on GPUs

2018 ◽  
Vol 18 (5) ◽  
pp. 21-43
Author(s):  
Dusan Bikov ◽  
Iliya Bouyukliev
Keyword(s):  
Boolean Functions ◽  
Parallel Execution ◽  
Experimental Results ◽  
Walsh Transform ◽  
Sequential Algorithm ◽  
Differential Uniformity ◽  
Walsh Spectrum

Abstract Some of the most important cryptographic characteristics of the Boolean and vector Boolean functions (nonlinearity, autocorrelation, differential uniformity) are connected with the Walsh spectrum. In this paper, we present several algorithms for computing the Walsh spectrum implemented in CUDA for parallel execution on GPU. They are based on the most popular sequential algorithm. The algorithms differ in the complexity of implementations, resources used, optimization strategies and techniques. In the end, we give some experimental results.

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